An Israeli regulation prohibits “any religious ceremony” at the wall “not in accordance with the custom of the holy site and which offends the sensitivities of the worshipers.” Women wearing prayer shawls have been deemed unduly provocative because of the biblical injunction against women wearing men’s clothing and vice versa.

This episode may sound like some obscure tribal fight, and it is — we Jews excel at obscure tribal fights. But the dispute also echoes larger religious battles — not only within Judaism but also within Islam and the Catholic Church.

The common chord of orthodox religions’ struggle against the tides of modernity involves women, specifically whether to loosen doctrinal restrictions on women. So it was a fitting coincidence that the latest skirmish involving the group known as Women of the Wall occurred the same day that Pope Benedict XVI announced his abdication.

One of the central questions facing the Catholic Church — one of the stances on which Benedict was most unrelenting and on which his successor is likely to be similarly rigid — is the ordination of women.

The rational move, for a church facing a dire worldwide shortage of priests, would be to expand the pool of potential candidates. This concession to modernity would not be resisted by the faithful; polls in the United States and abroad show strong majorities in support of women serving as priests.

Instead, the church has been moving in the opposite direction, hardening the teaching against ordaining women priests and declaring this doctrine “set forth infallibly,” incapable of being changed. In 2010, the church decreed that the “attempted ordination of women” was among the list of most grievous crimes under church law, on a par with priests sexually abusing minors.

The reasoning behind this decree seems to boil down to biblical originalism: Because Jesus chose only male apostles, and because only men have served as priests ever since, only men can serve as priests in perpetuity.

The church gets to set the church’s rules; when you’re pope, “because I said so” is a rather convincing — indeed, infallible — argument. The more interesting question is what fuels this rigidity.

Why is the idea of a female priest so threatening? Why is the notion of a woman wearing a prayer shawl — after all, religious types usually worry about women not being covered enough — so provocative? As with women as Catholic priests, there is no positive biblical injunction against this practice, although, again as with female priests, it’s contrary to tradition.

And why in the more extreme corners of Islam is the thought of a girl receiving an education, or a woman appearing alone or uncovered in public, so inflammatory?

That question is, I admit, a sudden shift, a marked rhetorical escalation. The pope is not the Taliban. Neither are the ultra-Orthodox rabbis. There is no comparison between their positions, however irrational and chauvinistic, and those of Islamic extremists.

But I would also suggest that the underlying impulses are not all that different: fear of encroaching modernity undermining doctrinal control.

That this reasoning is not necessarily conscious on the part of those seeking to maintain authority does not make it any less powerful. “I think it’s truly a deep-seated belief on the part of the male hierarchy that they have this profound theological obligation to keep it as it is,” Patricia McGuire, president of Trinity Washington University, told me.

The same can be said of the bizarre showdown over prayer shawls at the Western Wall. The tallit-wearing women did not seek to pray on the side of the wall that has been designated for men. And yet their actions — doing something common in my conservative synagogue — were deemed so threatening to public order that the police felt compelled to act.

To believe in religious liberty is to insist that the Catholic Church has the right to decide not to allow female priests, however backward this might be. To believe in religious pluralism is to insist that no single authority can dictate proper behavior. The Israeli government faces competing claims to a holy site. The solution cannot be for the Jewish state to arrest Jewish women for practicing their religion.